Singular trajectories in multi-input time-optimal problems: Application to controlled mechanical systems

TL;DR

This paper investigates the structure of singular trajectories in multi-input time-optimal control problems for mechanical systems, utilizing Lie algebra properties and Pontryagin's principle, with applications to underwater vehicle control.

Contribution

It introduces a novel analysis of singular extremals in mechanical control systems using Lie algebra properties and applies the theory to underwater vehicle control problems.

Findings

Characterization of singular extremals in mechanical systems

Application of Lie algebra properties to control trajectory analysis

Optimal control strategies for underwater vehicles

Abstract

This paper addresses the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems enjoy certain special properties. These properties are explored and are used in conjunction with the Pontryagin maximum principle to determine the structure of singular extremals and, in particular, time-optimal trajectories. The theory is illustrated with an application to a time-optimal problem for a class of underwater vehicles